Nucleation homogenous

An important approach to the study of nucleation of solids is the investigation of small droplets of large molecular clusters. Years ago, Turnbull showed that by studying small droplets one could eliminate impurities in all except a few droplets and study homogeneous nucleation at significant undercoolings [13]. 

F. F. Abraham, Homogeneous Nucleation Theory, Academic, New York, 1974. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Spontaneous (Homogeneous) Nucleation This process is quite difficult because of me energy barrier associated with creation of the interfacial area. It can be treated as a kinetic process with the... 

Since the critical supersaturation ratio for homogeneous nucleation is typically greater than 3, it is not often reached in process equipment. 

Nucleation The mechanism of crystal nucleation from solution has been studied by many scientists, and recent work suggests that—in commercial crystallization equipment, at least—the nucleation rate is the sum of contributions by (1) homogeneous nucleation and (2) nucleation due to contaci between crystals and a) other crystals, h) the walls of the container, and (c) the pump impeller. If is the net number of new crystals formed in a unit volume of solution per unit of time. 

Although Eqs. (18-28) and (18-29) have been adopted by many as a matter of convenience, they are oversimphfications or the very complex relationship that is suggested by Eq. (18-25) Eq. (18-29) implicitly and quite arbitrarily combines the effects of homogeneous nucleation and those due to contact nucleation. They should be used only with caution. 

It is imphcit that increasing the value of Ly will raise the supersaturation and growth rate to levels at which mass homogeneous nucleation can occur, thereby leading to periodic upsets of the system or cycling [Randolph, Beer, and Keener, Am. In.st. Chem. Eng. J., 19, 1140 (1973)]. That this could actually happen was demonstrated experimentally by Randolph, Beckman, and Kraljevich [Am. In.st. Chem. Eng. J., 23, 500 (1977)], and that it could be controlled dynamically by regulating the fines-destruction system was shown by Beckman and Randolph [ibid., (1977)]. Dynamic control of a ciystaUizer with a fines-destruction baffle and fine-particle-detection equipment... 

Control of a batch ciystaUizer is almost always the most difficult part and veiy often is not practiced except to permit homogeneous nucleation to take place when the system becomes supersaturated. If control is practiced, it is necessary to have some means for determining when the initial solution is supersaturated so that seed of the appropriate size, quantity, and habit may be introduced into the batch. Following seeding, it is necessaiy to limit the coohng or evaporation in... 

A common cause of a BLE T] in plants of the hydrocarbon-chemical industry is exposure to fire. With an external fire below the liquid level in a vessel, the heat of vaporization provides a heat sink, as with a teakettle evolved vapors exit tnrough the relief valve. But if the flame impinges on the vessel above the liquid level, the metal will weaken and may cause the vessel to rupture suddenly, even with the relief valve open. The explosive energy for a BLE T] comes from superheat. This energy is at a maximum at the superheat hmit temperature. (SLT is the maximum temperature to which a hquid can be heated before homogeneous nucleation occurs with explosive vaporization of the hquid and accompanying overpressure.) The SLT... 

When the nucleus is a liquid, the angle 6 is called tire wetting angle. It can be seen that the critical radius in heterogeneous nucleation is given by the same equation as tlrat for homogeneous nucleation, but the radius now refers... 

According to homogeneous nucleation dreory, dre critical Gibbs energy to form a nucleus is given by... 

The evolution of gases, such as in dre example given above of dre formation of CO(g) in dre U airsfer of sulphur between carbon-saturated iron and a silicate slag, requires dre nucleation of bubbles before dre gas can be eliminated from the melt. The possibility of homogeneous nucleation seems unlikely, and the more probable source of gas bubbles would either be at the container ceramic walls, or on detached solid particles of the containing material which are... 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

In this chapter we have shown that diffusive transformations can only take place if nuclei of the new phase can form to begin with. Nuclei form because random atomic vibrations are continually making tiny crystals of the new phase and if the temperature is low enough these tiny crystals are thermodynamically stable and will grow. In homogeneous nucleation the nuclei form as spheres within the bulk of the material. In... 

Fig. 7.5. Nucleation in solids. Heterogeneous nucleotion con take place at defects like dislocations, grain boundaries, interphase interfaces and free surfaces. Homogeneous nucleation, in defect-free regions, is rare.

Fig. 9.1. Rain falls when the water droplets in clouds turn to ice. This con only happen if the clouds are below 0°C to begin with. If the droplets are clean, ice can form only in the unlikely event that the clouds cool down to the homogeneous nucleation temperature of -40°C. When dust particles are present they can catalyse nucleation at temperatures quite close to 0°C. This is why there is often heavy rainfall downwind of factory chimneys.

Homogeneous nucleation occurs when, as a result of statistically random segmental motion, a few segments have adopted the same conformation as they would have in a crystallite. At one time it was considered that the likelihood of the formation of such nuclei was greatest just above the transition temperature... 

Homogeneous Nucleation a process by which gases interact and combine with droplets made up of their own kind. For instance, the collision and subsequent adherence of water vapor to a water droplet is a homogeneous nucleation. See nucleation. 

Nucleation a process by which a gas interacts and combines with droplets. See homogeneous nucleation. 

The process of homogeneous nucleation is determined by the formation of stable nuclei in a supersaturated solution. 

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